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On a variational method for univalent functions

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Abstract

In the paper, the construction of a variational method for univalent functions is suggested; this construction uses the factorization theorem. As a consequence, an analog of the Goluzin variational formula is obtained.

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References

  1. V. D. Erokhin, “On conformal transformations of rings and the fundamental basis of the space of functions analytic in an elementary neighbourhood of an arbitrary continuum,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.] 120(4), 689–692 (1958).

    MATH  Google Scholar 

  2. S. A. Gel’fer, “An extension of the Goluzin—Schiffer variational method to multiply-connected regions,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.] 142(3), 503–506 (1962).

    Google Scholar 

  3. G. M. Goluzin, “Variational method in conformal mapping. I,” Mat. Sbornik N. S. 19, 203–236 (1946).

    Google Scholar 

  4. V. V. Kozhevnikov, “Factorization of conformal mappings and variations of univalent functions,” Dokl. Ross. Akad. Nauk [Russian Math. Dokl.] 375(3), 305–306 (2000).

    Google Scholar 

  5. V. V. Kozhevnikov, “Piecewise univalent variations of second order,” in Geometric Analysis and Its Applications, Abstracts of Reports of the Volgograd Conference, (Izd. Volgograd Univ, Volgograd, 2004), pp. 80–82 [in Russian].

    Google Scholar 

  6. V. V. Kozhevnikov, “On a form of the direct variational method for univalent functions,” Izv. Vyssh. Uchebn. Zaved. Mat. [Russian Math. (Iz. VUZ)] 503(4), 28–38 (2004).

    Google Scholar 

  7. K. I. Babenko, The theory of extremal problems for univalent functions of class S, in Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.] (Nauka, Moscow, 1972), Vol. 101.

    Google Scholar 

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Original Russian Text © V. V. Kozhevnikov, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 2, pp. 240–250.

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Kozhevnikov, V.V. On a variational method for univalent functions. Math Notes 81, 213–221 (2007). https://doi.org/10.1134/S0001434607010245

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  • DOI: https://doi.org/10.1134/S0001434607010245

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